To solve the equation [tex]\(3x + 5y = 15\)[/tex] for [tex]\(y\)[/tex], we will follow these steps:
1. Isolate the term involving [tex]\(y\)[/tex]:
Begin by subtracting [tex]\(3x\)[/tex] from both sides of the equation to move the [tex]\(3x\)[/tex] term to the right side.
[tex]\[
3x + 5y - 3x = 15 - 3x
\][/tex]
Simplifying this, we have:
[tex]\[
5y = 15 - 3x
\][/tex]
2. Solve for [tex]\(y\)[/tex]:
Next, divide every term in the equation by [tex]\(5\)[/tex] to solve for [tex]\(y\)[/tex].
[tex]\[
\frac{5y}{5} = \frac{15}{5} - \frac{3x}{5}
\][/tex]
Simplifying this, we get:
[tex]\[
y = 3 - \frac{3}{5}x
\][/tex]
Therefore, the correct expression for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex] is:
[tex]\[
y = 3 - \frac{3}{5} x
\][/tex]
3. Match the obtained solution with the given options:
We should find which one of the given options matches our solution [tex]\(y = 3 - \frac{3}{5}x\)[/tex]:
A. [tex]\(y = 3(15 - 3x)\)[/tex]
B. [tex]\(y = 3 - \frac{3}{5}x\)[/tex]
C. [tex]\(y = 15 - 3x\)[/tex]
D. [tex]\(y = \frac{5}{3}x - 3\)[/tex]
Clearly, the correct option is:
[tex]\[
\boxed{B \; y = 3 - \frac{3}{5} x}
\][/tex]
